Electric measurements with constant current: A practical method for characterizing
dielectric films
José A. Giacometti, Célio Wisniewski, Paulo Antonio Ribeiro, and Walterley Araújo Moura
Citation: Review of Scientific Instruments 72, 4223 (2001); doi: 10.1063/1.1409564
View online: http://dx.doi.org/10.1063/1.1409564
View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/72/11?ver=pdfcov
Published by the AIP Publishing
Electric measurements with constant current: A practical method
for characterizing dielectric films
Jose´ A. Giacomettia)
Faculdade de Cieˆncia e Tecnologia, Universidade Estadual Paulista, 10060-900, Presidente Prudente, SP, Brazil
Ce´lio Wisniewski
Instituto de Fı´sica de Sa˜o Carlos, Universidade de Sa˜o Paulo, CP 369. 13566-970, Sa˜o Carlos, SP, Brazil
Paulo Antonio Ribeiro
CeFITec, Departamento de Fı´sica, Faculdade de Cieˆncias e Tecnologia, Universidade Nova de Lisboa. 2825-114 Caparica, Portugal
Walterley Arau´jo Moura
Escola Te´cnica Federal de Mato Grosso. 78005-390, Cuiaba´, MT, Brazil
~Received 13 February 2001; accepted for publication 26 June 2001!
This article assesses the use of the constant current~CC!method for characterizing dielectric films. The method is based on charging the sample with a constant current~current stress!and measuring the corresponding voltage rise under the closed circuit condition. Our article shows that the CC method is an alternative to the constant voltage stressing method to study the electric properties of nonpolar, ferroelectric, and polar polymers. The method was tested by determining the dielectric constant of polytetrafluoroethylene, and investigating the electric conduction in poly~ethylene terephthalate!. For the ferroelectric polymer poly~vinylidene fluoride!, it is shown that hysteresis loops and the dependence of the ferroelectric polarization on the electric field can be obtained. © 2001 American Institute of Physics. @DOI: 10.1063/1.1409564#
I. INTRODUCTION
Electric measurements can be performed by either ap-plying a voltage~voltage stress!to the sample and measuring the electric current, or by charging the sample with a con-stant current~CC! ~current stress!and measuring the voltage rise. CC sources have been available for many years in voltage/current source supplies.1 Current stress has a wide application in electrochemistry,2 breakdown measurements in semiconductors,3 scanning tunneling microscopy,4 and measurements of surface electric conductivity using the four-point method.5The CC approach has also been used in con-nection with corona charging of insulators. In the 1980’s, a corona triode was built which allowed dielectric samples to be charged with a CC, under an open circuit.6 – 8In addition to charging control, this corona triode permitted the investi-gation of electrical properties of polymers9,10 and even to obtain hysteresis curves for ferroelectric polymers.11 In this work, the CC method is applied in measurements under the closed circuit condition, i.e., with electroded samples.
The mathematical treatment of experimental data is not the same in voltage and current stresses. In controlled current experiments, equations are based on the known current, while in voltage controlled methods, they are based on the known voltage. The advantage of the CC is that the Maxwell total current equation can be, in some cases, analytically in-tegrated and the charge transport and trapping in insulators may be theoretically treated.9,12The connection between the
CC and voltage methods is briefly discussed in Ref. 13. More recently, the equivalence between hysteresis loops ob-tained with the CC and the Saywer–Tower methods was al-ready demonstrated.14 From the experimental point of view, another advantage of the CC method is that an ammeter is not required.
This article assesses the use of the CC method for char-acterizing dielectric films such as polymers. The CC control-ler circuit, designed to be used in combination with a com-mercial high-voltage ~HV! bipolar amplifier, is described. The setup is fully computerized allowing an electric current as low as a few nA to be monitored. The basic equations of the CC method are presented, which allows interpretation of the various types of measurements in dieletric films. Here, in particular, results will be discussed for the measurement of the dielectric constant in nonpolar/polar polymer samples and for hysteresis loops in ferroelectric polymers.
The article is organized as follows. In the Experiment section, Sec. II, samples, experimental conditions, the CC controller circuit, and its characteristics are described. The basic equations of the CC method are given in Sec. III and in Secs. IV–VI, results are presented for different polymers. Final remarks are highlighted in Sec. VII.
II. EXPERIMENT
A. The constant current setup and the CC controller characteristics
The CC method consists in charging the sample with a constant electric current, I0, and measuring the resulting a!Electronic mail: www.polimeros.if.sc.usp.br and [email protected]
4223
voltage rise, V(t), on its electrodes. The schematic diagram of the measuring setup is illustrated in Fig. 1. It consists of a homemade constant current controller, a HV bipolar ampli-fier TREK 610C~maximum voltage of610 kV!, the dielec-tric sample, and a personal computer with digital-to-analog
~D/A!and analog-to-digital ~A/D! converters from National Instruments ~12 bits of resolution!. The controller circuit, shown in Fig. 2, is the most critical part of the setup. It includes a current amplifier/current-to-voltage converter, CA, an error amplifier, E, and an integrator, I, that operates in the proportional–integrative mode~PI!. A follower amplifier, F, was also added to the circuit allowing the current to be moni-tored during the experiments. R1 and C1 allow adjusting the current sensitivity and the variable resistor, RX, allows ad-justing the integrator time constant. The error amplifier E, with a unitary gain, gives the signal difference between the reference voltage VR, and the measured signal, V0. The
am-plifier CA converts the current I0 into the voltage V0. If
V02VR.0, the integrator I decreases its output, then de-creasing V(t) and I0. If V02VR,0, then V(t) and I0 are
increased, forcing V05VRand, thus, the current in the circuit to be constant.
The computer software, written in Visual Basic for
Win-dows, allows setting the value of the reference voltage VR
~50 mV corresponds to 1 nA! to the CC controller via the D/A computer interface. Via computer, the HV output of the Trek amplifier can be activated remotely, and the switch S may also be actuated, starting and stopping the operation of the CC controller. The experimental data, V(t) and I0, are
collected via the A/D interface, displayed graphically on real time on the computer screen and stored in the hard disk. With the software, the measurement may be discontinued auto-matically~opening S and turning the HV supply off!, when-ever the sample breaks down.
The setup can be operated in the voltage interval of
610 kV and one of its capabilities is to reverse the polarity of the current without discontinuing the measurement. Con-trol experiments demonstrated that the switching time from one polarity to another is less than a second, much smaller than the several minutes of a typical measurement. The con-troller can be operated with a current of a few nA and above, within a few percent of fluctuation.
B. Experimental conditions and samples
Samples of polytetrafluoroethylene, Teflon polytetrafluo-roethylene~PTFE!, were supplied by Dilectricx, USA.
Poly-~vinylidene fluoride!, PVDF, samples were biaxially stretched and supplied by Kureha, Japan, and samples of poly~ethylene terephthalate!, PET, were supplied by Rhodia, Brazil. The sample thickness used in this work was 12mm. The sample electrodes of PVDF and Teflon PTFE, were de-posited by thermal evaporation of aluminum in a vacuum, had diameter of 1 cm corresponding to an area of 0.8 cm2. In the case of PET samples, the electrodes had 2 cm of diameter corresponding to the area of 3.1 cm2. The sample holder al-lows one to perform measurements in a high vacuum and the temperature can be controlled within 60.5 °C.
III. CC BASIC EQUATIONS
The Maxwell total current density J(t) in a dielectric slab in planar geometry is given by
J~t!5JC~t!1 dD~t!
dt , ~1!
where JC(t)5(1/L)*0
LJ
C(x,t)dx and D(t)
5(1/L)*0LD(x,t)dx are mean values of the conduction cur-rent and electric displacement~x is the coordinate and L the sample thickness!. The electric displacement is given by
D~t!5eE~t!1P~t!, ~2!
where e is the instantaneous dielectric permittivity, and E and P are the electric field and the electric polarization, re-spectively. In general, the electric polarization could be time delayed or ferroelectric, which has a nonlinear dependence on the electric field.
For the constant current case, J(t)5J0, Eq.~1!becomes
J05edE~t!
dt 1 d P~t!
dt 1JC~t! ~3!
or
FIG. 1. Schematic diagram of the measuring setup. V(t) is the measured voltage and I0is the constant current.
FIG. 2. Circuit diagram of the current controller. CA is the current amplifier, E an error amplifier, and I the integrator. The circuit component values are
R15100 MV, R25500V, R3510 kV, R515 kV, 1 kV,Rx,10 MV,
C15100 pF, C2510 nF, and C35100 nF. The integrated circuits are CA15CA3140, E5LF356N and I5LF356N.
4224 Rev. Sci. Instrum., Vol. 72, No. 11, November 2001 Giacomettiet al.
I05C
dV~t!
dt 1A d P~t!
dt 1IC~t!, ~4!
with the voltage on the sample given by V(t)5E(t)L, sample capacitance C5eA/L and IC(t)5AJC(t), I05AJo, and A is the sample area. It is worth mentioning that Eq.~4!
can be analytically integrated, in some cases, if P(t) and IC(t) are known. For further details see Refs. 9 and 12.
When samples are nonpolar @P(t)50# and there is no electric conduction~IC(t)50!, Eq.~4!becomes
V~t!5LJ0t
e 5
I0t
C , ~5!
leading to a linear voltage increase with a rate equal to I0/C. One can infer from Eqs.~4!and~5!that the rate I0/C will be the upper limit since the presence of polarization or conduc-tion will produce a decrease on the rate of the voltage in-crease.
IV. PERFORMANCE OF THE CC METHOD
For evaluating the performance of the CC method for polymers such as Teflon PTFE, the voltage buildup was mea-sured and the dielectric constant determined. Because Teflon PTFE is a nonpolar polymer, d P(t)/dt50 in Eq.~4!, thus
I05C
dV~t!
dt 1IC~t!. ~6!
Figure 3 shows experimental points corresponding to the voltage increase for 12mm thick Teflon PTFE samples, plot-ted as a function of the charge density Q(t)5J0t, for
differ-ent CC currdiffer-ent amplitudes. It is well known that Teflon is a very highly insulating material in which the electric conduc-tion could be neglected for moderate electric fields, thus, Eq.
~6! is reduced to Eq. ~5!. In fact, the experimental data V(t)3Q(t) in Fig. 3 show that the voltage increases linearly up to 200 V, corresponding to an electric field of 17 MV/m.
From the slopes, the relative dielectric constant was calcu-lated and the results are plotted in the inset of Fig. 3 as a function of I0. The deviation from k52.05 increases for
small amplitudes of I0, since the conduction current can not
be neglected when compared with the displacement current
@see Eq. ~1!#. For comparison, the full line in Fig. 3 was plotted using Eq. ~5!. Calculation assumed that the sample had a relative dielectric constant, k5e/e052.05, which is
typical for Teflon PTFE. Similar results for polyfluoroethyl-ene propylpolyfluoroethyl-ene, Teflon FEP,~not shown here!were obtained. After the initial, linear increase, the voltage reached the steady state~not shown in the Fig. 3!, i.e., a saturation value for the PTFE samples. At the steady state dV(t)/dt50, con-sequently, the electric conduction through the sample is equal to the charging current@cf. Eq.~4!#. CC measurements in the corona charging of FEP samples were described in our previous papers.15–18For example, when samples were nega-tively, corona charged results were explained using theoreti-cal models assuming a near trapping filling limit.16,17
V. APPLICATION OF THE CC METHOD TO A FERROELECTRIC POLYMER
Figure 4 shows the voltage buildups in a PVDF sample charged with a positive current density of 8.0 mA/m2 ~I0
580 nA!. Curve I corresponds to the voltage increase when the ferroelectric switching occurs. It increases linearly at the very beginning at a rate equal to I0/C, where the electric
capacitance, C, is equal to 0.75 nF in good agreement with
k513, usually found in the literature.19 After this initial, linear increase, the curve shows a quasiplateau, and finally increases steeply again. The quasiplateau region is related to the ferroelectric dipole switching which leads to the neutral-ization of the incoming charge. In Curve II @sample poled with the same current polarity as in Curve I but the current density is 2.5 mA/m2~I0520 nA!#, the potential grows more
rapidly since switching does not occur, i.e., in this case, the incoming charge is not neutralized by the switching of the ferroelectric polarization. In our measurements, we took care to reduce the electric conduction in PVDF to a negligible value by performing the measurements in high vacuum,20 i.e., JC(t)50 in Eq.~3!.
FIG. 3. Voltage buildup plotted versus the charge density, Q(t)5J0t,
trans-ferred to the Teflon PTFE samples charged with different values of current. Inset: the dielectric constant determined from the voltage build rate for different charging currents. Sample thickness is 12mm.
FIG. 4. Potential buildups for a PVDF ferroelectric sample. Curve I corre-sponds to the voltage increase during the switching of the polarization. Curve II sample charged with the same voltage polarity without polarization switching. Sample thickness is 12mm.
The ferroelectric hysteresis loop, with the electric dis-placement D versus the electric field E, can be obtained if the electric conduction in the samples can be neglected. From Eq. ~1!, with JC(t)50, the electric displacement is D(t)5I0t. Since E(t)5V(t)/L, by eliminating the time one
can obtain the D3E loops. For obtaining the hysteresis loops, experimental measurements are performed continu-ously, i.e., after a positive charging, the polarity of the elec-tric current is reversed. Figure 5 displays the resulting hys-teresis plot. A slow increase of D versus E in the range of very high fields is seen, which is due to the contribution of the displacement current, CdV(t)/dt @see Eq.~4!#. Thus, in order to obtain loops of electric polarization, P3E, it is necessary to subtract theerelated contribution, i.e., the dis-placement current is subtracted from the total current. Re-sults with the CC method agreed very well with those ob-tained from the Sawyer–Tower setup ~applying a sinusoidal or a triangle voltage!.14 It was also shown that the CC method was suitable for determining the dependence of the stable ferroelectric polarization on the electric field in PVDF samples.20 To do it, successive charging experiments were performed with the same polarity. Experimental procedures and results are discussed in detail in Ref. 20.
VI. ELECTRIC CONDUCTION IN PET
Another possible application of the CC method is the study of electric conduction in polymers. As an example, we will present results for PET. Figure 6 shows the buildup of the voltage for PET samples charged with a CC current den-sity of 63.6mA/m2 ~I0520 nA! at various temperatures.
Measurements showed that after the linear increase V(t) reached the steady state, where the CC current impinging on the sample is equal to the conduction current through the sample. Lower values of the saturation voltage indicate higher conduction.
We investigated the dependence of the steady state volt-age on the charging current for different values of tempera-ture. Analysis of data, see Fig. 7, indicated that the conduc-tion current obeys the Poole–Frenkel law, i.e., a linear dependence of the logarithm of the electric conductivity
~J/E!versus
A
E. In the Poole–Frenkel model, the slope of J/E versusA
E is equal tobF/2kT, where k is the Boltzmannconstant, T is the absolute temperature, and bF
5(e3/pe)1/2 is the Poole–Frenkel constant ~e is the elec-tronic charge!. From the plot of Fig. 7, reasonable values for the dielectric constant were obtained,21 confirming that the Poole–Frenkel conduction model is appropriate to explain the experimental results with the CC method. This is not surprising since it is well known that the Poole–Frenkel con-duction plays an important role in PET polymer.22
VII. DISCUSSION
Measurements with constant current are frequently used to control the corona charging of insulators, usually under the open circuit condition.9According to our knowledge, this work is pioneering because it assesses the electric character-ization of different dielectric materials using the CC method. Our experimental setup was designed for measurements us-ing electroded samples, i.e., under the closed circuit condi-tion. Basic equations of the CC method are the same em-ployed for the CC open circuit in the corona charging. The application of our CC method to investigate dielectric prop-erties of insulating films was shown. When charged up to moderate electric fields, Teflon PTFE displays a linear in-crease in voltage, which allows the dielectric constant of the sample to be measured as a test procedure for evaluating the
FIG. 5. Hysteresis loop of the electric displacement, D, versus the electric
field, E, for the PVDF sample 12mm thick. FIG. 6. Voltage buildup for PET samples for different temperatures. The CC electric current was 20 nA. Sample thickness is 12mm.
FIG. 7. Dependence of the electric conductivity on the square root of the electric field~at steady state condition!for different temperatures. Sample thickness is 12mm.
4226 Rev. Sci. Instrum., Vol. 72, No. 11, November 2001 Giacomettiet al.
CC method. For PVDF, we show that the switching of the ferroelectric polarization can be observed in successive mea-surements with the same current polarity. We also showed that hysteresis loops of PVDF samples can be obtained if measurements are performed continuously, i.e., the polarity of the current is reversed while the current is continuously measured.14 Finally, it was shown that the electric conduc-tion in PET obeys the Poole–Frenkel law in agreement with published data.21,22
Theoretical models for CC measurements are already available and described in the literature12 for several cases such as free charge injection and charge injection in the pres-ence of trapping. Such models were originally applied to corona charging measurements under open circuit but they are the same for closed circuit measurements. The main dif-ference resides in the fact that in corona measurements, one surface usually has no electrode and corona ions are depos-ited on it. In contrast, our measurements are performed with samples having two electrodes that could produce, for ex-ample, different charge injection processes.
Overall, we stress that the CC method is a convenient method for characterizing dielectrics. Its main advantage is related to the theoretical interpretation of experimental data since the differential equations of the charging transport can be analytically integrated.
ACKNOWLEDGMENTS
FAPESP, CNPq, and CAPES ~Brazil! financially sup-ported this work.
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